Image display devices that horizontally and vertically scan a projection surface with laser light and thereby display an image thereon are known (for example, Japanese Patent Publication No. 2007-121538A and Japanese Patent Publication No. 2008-268645A).
FIG. 1 shows the structure of a scanner of an image display device.
Referring to FIG. 1, the image display device includes light source 121; condenser lens 122 that condenses a laser beam emitted from light source 121 on projection surface 124; and scanning mirror 123 that scans projection surface 124 with the laser beam condensed by condenser lens 122.
Regularly, the size of each pixel of a displayed image depends on the diameter of the beam spot on projection surface 124. Thus, if condenser lens 122 and projection surface 124 are set such that the beam waist of the condensed laser beam is positioned at projection surface 124, the diameter of the beam can be decreased and a high-resolution image can be obtained.
However, since the optical path length of the laser beam from scanning mirror 123 to projection surface 124 changes based on the scanning angle of scanning mirror 123, the beam waist may not be positioned at projection surface 124 depending on the position thereon. In this case, the resolution becomes lower on a part of the screen.
Next, the reason why the resolution becomes lower on a part of the screen will be described.
FIG. 2 schematically shows that the optical path length and the beam waist change based on scanning angle θ.
Assuming that the effective diameter (radius) of scanning mirror 123 is denoted by w, the propagation distance is denoted by z, and the radius of the beam waist formed at a distance where the amplitude value becomes 1/e of the maximum value is denoted by ωo, the following equations 1 and 2 are satisfied. In these equations, λ is the wavelength of the laser beam; and π is a circular constant. The beam numerical aperture is given by ω/z.[Mathematical Expression 1]ω2=ω02·{1+(z/a)2}  (Equation 1)[Mathematical Expression 2]a=π·ω02/λ  (Equation 2)
It is now assumed that the beam diameter (radius) on projection plane 124 is ω0 when scanning angle θ is zero and the beam waist is arranged on light path length L(0). Light path length L(0) is the distance from the surface of scanning mirror 123 to projection plane 124 on the light path of the central light beam of the laser beams. Projection distance f is the distance from condenser lens 122 to projection plane 124, and is determined by the focal length of condenser lens 122. When the distance from a principal point of condenser lens 122 to the surface of scanning mirror 123 is denoted by d, then light path length L(0) is a value which is obtained by subtracting distance d from projection distance f.
The distance from the surface of scanning mirror 123 to projection plane 124 on the light path of the central light beam of the laser beam when scanning angle θ is greater than 0, is assumed to be light path length L(θ). Then, light path length L(θ) is expressed by the following Equation 3.[Mathematical Expression 3]L(θ)=L(0)/cos θ  (Equation 3)
If scanning angle θ is greater than 0, since optical path length L(θ) becomes greater than optical path length L(O), propagation distance z in equation 1 increases. As a result, the beam diameter (radius) increases from 2ω0 to 2ω(L(θ)). As scanning angle θ increases, the beam diameter (radius) on projection surface 124 becomes large. As a result, the size of each pixel increases and thereby the resolution of the image decreases in the circumferential region of the screen.
In the foregoing image display device, if a varifocal lens is used as condenser lens 122 and the focal length of the varifocal lens is controlled based on scanning angle θ such that the beam waist is positioned at projection surface 124, a high-resolution image can be equally displayed on the entire screen.
The varifocal lens is composed for example of a condenser lens, a divergent lens, and an actuator that moves the condenser lens in the optical axis direction. When the actuator moves the condenser lens, the distance between the condenser lens and the divergent lens changes and thereby the focal length changes.
FIG. 3A schematically shows the arrangement of the varifocal lens having a long focal length, whereas FIG. 3B shows the arrangement of the varifocal lens having a short focal length.
As shown in FIG. 3A, as distance d between condenser lens 130 and divergent lens 131 becomes short, back focus BF becomes long. In contrast, as shown in FIG. 3B, as distance d between condenser lens 130 and divergent lens 131 becomes large, back focus BF becomes short.
Back focus BF is expressed by the following equation 4.[Mathematical Expression 4]BF={f1−d}·f2/(f1+f2−d)  (Equation 4)
where f1 denotes the focal length of condenser lens 130; and f2 denotes the focal length of divergent lens 131.
As technologies for the foregoing varifocal lens, Japanese Patent Publication No. 2007-121538A describes a focusing optical system that is composed of a combination of a condenser lens and a divergent lens and Japanese Patent Publication No. 2008-268645A describes a structure in which an actuator moves a condenser lens in the optical axis direction.